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<h1>1</h1>

<p>\[ 
(4.2) p(X) = \frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}
 \]</p>

<p>So, \( \frac {p(X)} {1 - p(X)} \)</p>

<p>\[ 
= \frac {\frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}}
        {1 - \frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}}
\\
= \frac {\frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}}
        {
          \frac {1 + e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}
          - \frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}
        }
\\
= \frac {\frac {e^{\beta_0 + \beta_1 X}} {1 + e^{\beta_0 + \beta_1 X}}}
        {\frac {1} {1 + e^{\beta_0 + \beta_1 X}}}
\\
(4.3)    \frac {p(X)} {1 - p(X)} =e^{\beta_0 + \beta_1 X}
 \]</p>

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